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It is well known that the Cox-Ingersoll-Ross (CIR) stochastic model to studythe term structure of interest rates, as introduced in 1985, is inadequate formodelling the current market environment with negative short interest rates.Moreover, the diffusion term in the rate dynamics goes to zero when short ratesare small; both volatility and long-run mean do not change with time; they donot fit with the skewed (fat tails) distribution of the interest rates, etc.The aim of the present work is to suggest a new framework, which we call theCIR\# model, that well fits the term structure of short interest rates so thatthe market volatility structure is preserved as well as the analyticaltractability of the original CIR model.

On The Calibration of Short-Term Interest Rates Through a CIR Model